I suspect the problem here is that the first CD you made - the one that worked in your car - was an Audio CD, and the second one you made was a data CD containing audio tracks (two different disc formats).
Are you using the in-built CD burning capabilities of Windows Media Player or are you using a different program to actually burn the discs (like Nero or Roxio etc)? In Windows Media Player, when burning a disc, make sure that the box on the left column (which shows what's going to go onto the CD displays "Audio CD" because it can be changed to DataCD and HighMAT Audio, and neither of those will work in a traditional car CD player unless it specifically supports them.
Also, when writing these discs, did you use CD-R discs in both cases? For example, if you tried to use a CD-RW disc instead of a CD-R one the second time 'round, that might also explain why it only worked in your PC, since most audio CD players don't read from CD-RWs (unless otherwise stated).